Question: Simplify the following expression: $r = \dfrac{1}{7k} + \dfrac{1}{3k}$
Explanation: In order to add expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $7k$ and $3k$ $\lcm(7k, 3k) = 21k$ $ r = \dfrac{3}{3} \cdot \dfrac{1}{7k} + \dfrac{7}{7} \cdot \dfrac{1}{3k} $ $r = \dfrac{3}{21k} + \dfrac{7}{21k}$ $r = \dfrac{3 +7}{21k}$ $r = \dfrac{10}{21k}$